FRACTAL COMPRESSION TECHNIQUE FOR COLOR IMAGES USING VARIABLE BLOCK
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1 ISSN: (ONLINE) ICTACT JOURNAL ON IMAGE AND VIDEO PROCESSING, NOVEMBER 017, VOLUME: 08, ISSUE: 0 DOI: /jvp FRACTAL COMPRESSION TECHNIQUE FOR COLOR IMAGES USING VARIABLE BLOCK Nsar Ahmed 1 and Syed Abdul Sattar 1 Department of Electroncs and Communcaton Engneerng, Mewar Unversty, Inda Department of Electroncs and Communcaton Engneerng, Nawab Shah Alam Khan College of Engneerng and Technology, Inda Abstract The man ntenton of Fractal Compresson s to reduce the sze of mage and mantan good level of ther reconstructed mage. A major ssue n Fractal Compresson s decrease n mage qualty, compresson rato and PSNR. To overcome these ssues we employ Fractal transformaton wth entropy codng. There are two phases n the proposed approach. In the frst phase color mages are separated nto three RGB planes usng varable range block sze. In second phase by applyng the nverse transform and teratve functons the mage s restored. It s observed that the results are mprovng n fractal compresson for both gray mages as well as color mages. In ths work hgh CR and PSNR s observed compared to fxed block range and other exstng methods. The proposed work yelds better CR of 0 and hgh PSNR. Keywords: Fractal Compresson, Varable Block Sze, CR, PSNR 1. INTRODUCTION s are nterpreted as accumulaton of bts (a bt s a bnary unt of nformaton) and stored n dgtal meda storages n the computer. These bts are denoted as pxels or ponts that form the pcture elements. A human eye progresses large amount of nformaton of approxmately 8 mllon bts to create a sngle mage. Profuse pxels consttute the formaton of a reasonable qualty mage whch, the eye arbtrates the 8 mllon bts from yes and no answers to develop the mage progresson. Redundancy of the pxels enrches the absorpton capablty of the eye to nterpret the mages nto promnence, thus makng them more apprehensble. Ths redundancy can be manpulated and reduced through algorthms for optmum storage and restored for recovery. An mage can be alternated n many ways that are ether not notced by the human eye or do not contrbute to the decay of the mage. The current most famous method of mage compresson depend on elmnaton of hgh frequency wavelengths of the sgnal and storng only the low frequency components. Fractal based mage compresson (FIC) technque explot redundancy due to self-smlarty propertes n mages to acheve compresson [1]. A doman optmzaton technque n fractal mage compresson [] deals wth reducng complexty and ncreasng accuracy that s range and doman block algnment and matchng. Fractal Compresson s a separated mage that can be a part of parts; the man motto of the fractal mage compresson s to reduce the redundancy or the mage as well as mage rrelevance to store [3]. Moreover mage compresson s a transformaton called relatve transformaton. Fractal mage compresson s proposed n [4] based on Lossy compresson prncple whch provdes a very hgh compresson rato by completely elmnatng the redundant nformaton. The drawback of ths technque s the degradaton durng reproducton of the mage because of nsuffcent pxels for the fller sectons comprsng the redundant pxels. The mage whch s reconstructed contans degradaton relatve to the orgnal mage because the compresson scheme completely neglects the redundant nformaton and s more capable for achevng hgher compresson [5]. Fractal mage compresson (FIC) s based on the theory of Iterated Functon System (IFS) whch s used to represent the self-smlartes of the mages and s represented as a fnte set of contracton mappng for each mage that has the fxed pont whch s dentcal to the mage tself [6]-[8]. Fractal mage compresson (FIC) seems to be one of the favorable methods of lossy mage compresson due to ts advantages lke resoluton ndependence, hgh compresson rato, and fast decompresson [9]. Ths technque was ntally proposed by Jacqun and s based on the method of lossy compresson. Here the mages are consdered to be fractals rather than pxels, whch wll be manly sutable for natural mages for encodng, analyzng wth other mage compresson methods [10], [11] Suggested another system focused In the current scenaro, fractal mage compresson plays a major role n research areas, t s one of the knd of modern mage compresson technque coeffcents. Gohar and Habb [1] suggested n mage compresson two dfferent processes s carred out namely encodng and decodng. In encodng secton the orgnal mage takes as an nput and after processng the compressed mage wll be ts output but n decodng secton the process s carred out n reversble order. In the event that the neghborhood heghts are not fulflled, the second phase of the calculaton s completed keepng n mnd the end goal to nvestgate further lkenesses from the complete pcture. Kharate and Patl [13] proposed fractal compresson process through the self-smlar propertes n varous fractons of mages whch reles on the fact that the mage parts are often resembles other parts of the same mage. Sekhar and Aruna [14] proposed a fractal s a rough or fragmented geometrc shape that can be subdvded nto parts, each of whch s reduced/sze copy of the whole. Khall [15] found a major drawback n Fractal mage compresson (FIC), where encodng of fractals s very complex, compressng tme s very hgh due to ts complexty and consumpton of tme to search for the best matchng block and more powerful. Anson [16] has recommended the IFIC usng range block sze. Barnsley and Hurd [17] have recommended applyng the transformaton teratvely on the random ntal mage and the result wll be re-arranged as the orgnal mage. Banu [18] has proposed an effcent search of the doman pools for color mage compresson usng Genetc Algorthm (GA). The proposed method reduces the codng process tme and ntensve computaton tasks. qualty factor, compresson rato and codng tme are analyzed n ths approach and comparatve results are obtaned but ths method s sutable for only lmted categores lke facal, buldng and vegetable mages. 1639
2 NISAR AHMED AND SYED ABDUL SATTAR: FRACTAL COMPRESSION TECHNIQUE FOR COLOR IMAGES USING VARIABLE BLOCK. FRACTAL COMPRESSION Fractal compresson s one of the popular demandng research feld n the current trend, manly t deals wth the mages, vdeo sequences, graphcs, anmatons etc. Fractal compresson s one of the knd of lossy mage compresson technque, here t wll partton the mages nto blocks then perform some transformatons and then compress t. Normally based on lossy compresson, the compresson rato wll be hgh but the qualty of the mages wll not attan the expected results and there wll be a loss of nformaton s too. There are many technologes developed n dfferent research areas to mprove the mage qualty whle compressng the mages. In mage compresson consumpton of tme s more n encodng and decodng. There are some lmtatons exstng too. Ths has motvated us to develop an effcent compresson technque for color mages to enhance hgh compresson rato and PSNR. Varous compresson algorthms are used to reduce the sze of the mages wthout reducng the qualty of mages [19]. Algorthms lke embedded zero wavelet algorthm, convergent algorthm, Fuzzy vector quantzaton algorthm etc. are used prevously to compress the mages wth hgh qualty [0]. 3. PROPOSED ALGORITHM The man objectve of ths research s to compress the mage wth hgh rato and ncrease the PSNR of the encodng phase Step 1: Dvde color mage nto sub wndows. Each sub wndow block s called R- block. Step : For each R-block, fnd a Doman block, whch most lkely represents current R-block after a certan transform. Step 3: For every R-block, fnd D-block from D-pool whch s most lkely parallel to t. Crop the D-block sze to the sze of R-block by Shrnk operaton and, mark the D-block as D-block after Shrnk operaton s appled. Transpose the D- block by usng the followng eght relatve transformaton equaton matrces proposed by Jacqun. The eght relatve transformatons matrces are represented n the equatons as follows, a Consder T = [aj]n wth n = where 1 (,j), a a 11 1 a 1 Relatve transformatons matrces can be represented wth the followng Eq.(1) to Eq.(8),. 1 f j T 0 s a j (1) 0 else j 1 f j 0 else T 1 s a j () 1 f j T s a j (3) 0 else j 1 f j 0 else T 3 s a j (4) T 4 s a j 1 f j 0 T 5 s a j j 1 else 1 f j 0 T 6 s a j else 1 f j 0 j else (5) (6) (7) 1 f j T 7 s a j (8) 0 else Above eght relatve transformaton blocks are generated for each D-block and these blocks are composte new D-pool. Compare each R-block wth the blocks whch are n D- pool and obtan nearly all lke block. The parallelsm can be measured wth normal conflct MSE usng the Eq.(9). MSE XkDk Yk I Rk (9) where X and Y are the coeffcents and should have the values for makng the MSE mnmum. The X k and Y k are represented n Eq.(10) and Eq.(11) respectvely, X k = B Dk, Rk Dk, I Rk, I B Dk, Rk Dk, I Rk, I Dk, I Y k = B (10) (11) W = {D k(x,y), T k, X k, Y k} (1) where R k represents the relatve transformaton W for each R- block. Fractal mage codng, the orgnal mage s segmented nto non-collaboratng regons called range blocks and collaboratng regons called domans blocks. For each range block affne transformatons gven n the Eq.(13) s used to match as best doman block. x a b 0 x e W y c d 0 y f z 0 0 s z o (13) where S controls the contrast and 0 controls the brghtness and a, b, c, d, e, f denote the eght symmetres such as dentty, reflecton about md-vertcal and horzontal axs, frst and second dagonal. The Fg.1 s the proposed fractal mage compresson. 1. Partton each plane mage nto non-overlappng blocks, called Range or R-block.. Select the maxmum Range block of sze (R max) as 16 or 8 and mnmum block of sze (R mn) of 4 or 8. R-blocks are compared wth domans from the doman pool, whch are double the range sze. 3. A wndow sze of α α s slded on 3 mages n α/ or α/4. The pxels are averaged n groups to reduce to the sze. 4. After parttonng and transformaton, fractal encodng fnds sutable canddate from all blocks to encode any partcular R block. 1640
3 ISSN: (ONLINE) ICTACT JOURNAL ON IMAGE AND VIDEO PROCESSING, NOVEMBER 017, VOLUME: 08, ISSUE: 0 5. To ncrease encodng speed classfcaton of sub-mage nto upper rght, upper left, lower rght and lower left quadrants s done as shown n Fg.. It s shown that n any one of the three ways as canoncal orderng [1]. Parttonng Fg.1. Proposed Fractal Compresson Technque Fg.. Arrangement of Sub Blocks s Classfcaton Schemes are Sutable Doman Fractal Encoder Compressed Fractal Decoder Decompressed α 1 α α 3 α 4 α 1 α α 3 α 4 α 1 α α 3 α 4 Major Class 1: α 1 > α > α 3 > α 4 Major Class 1: α 1 > α 4 > α > α 3 Major Class 1: α 1 > α > α 4 > α 3 Entropy of codng s used to acheve fractal compresson for mappng the range block to the doman block n the codng process. 4. RESULTS AND DISCUSSION Doman Pool Selecton of transforms To fnd the effectveness of the proposed method by means of the expermental results. The Satellte urban and rural mages are reduced to standard sze The standard Lena mages of sze 5151 has been used for fractal compresson analyss. The frst phase conssts of applyng color and gray mages to a set of fve mages. We have used fve dfferent test mages n our experment. In the fnal phase we have calculated the CR and PSNR wth the resultant mages. The mageres are subjected to fractal compresson scheme by usng the varable range block sze for three cases namely, a) R max = 16 and R mn = 4 b) R max = 16 and R mn = 8 c) R max = 8 and R mn = 4, Three dfferent varable range methods are dsplayed n Table.1 and Table., respectvely. The novelty s, the proposed method s appled on both grey level and color mages. The proposed method gves the comparable results when appled on both color and grey mages. It s seen from Table.1 that the CR and PSNR values derved from Lena, Satellte Rural, Rose, Satellte and Brd mageres do not show sgnfcant dfference between the CR and PSNR values. However, Table.1 clearly demonstrates that CR and PSNR values derved for the Lena and other mageres show maxmum values for case where the varable range block sze R max = 16 and R mn = 8. It s clearly seen from Table.1 and Table. shows for Color and Grey mages values for CR and PSNR for all the types of mageres. The varable range block szes shows hgher CR and PSNR compared to fxed and other methods. Ths comparson s shown n Table.3, Table.4, Table.5, and Table.6, respectvely. Test s Table.1. CR and PSNR of Test Color s Rmax =16 and Rmn = 4 Rmax =16 and Rmn = 8 Rmax = 8 and Rmn = 4 CR PSNR CR PSNR CR PSNR Lena Satellte Rose Satellte Brd Test s Table.. CR and PSNR of Test Gray s Rmax=16 and Rmn = 4 Rmax=16 and Rmn = 8 Rmax=8 and Rmn = 4 CR PSNR CR PSNR CR PSNR Lena Satellte Rose Satellte Brd Varable range block sze R max = 16 and R mn = 8 are shown n Fg.3-, Fg.4-, Fg.5-, Fg.6-, Fg.7- and Fg.8-. These are the reconstructed mages for Color and Grey Lena, Rose, urban satellte, brd and rural satellte mageres. As seen n the fgure and tables that the proposed IFIC method for the mages of Lena, Brd, Satellte Rural, Rose and urban satellte gves sgnfcantly large CR values exhbts a very good qualty of the reconstructed mageres. 1641
4 NISAR AHMED AND SYED ABDUL SATTAR: FRACTAL COMPRESSION TECHNIQUE FOR COLOR IMAGES USING VARIABLE BLOCK Fg.7. Results of Brd gray mage orgnal gray brd reconstructed brd mage Fg.3. Results of Lena color mage Lena reconstructed Lena mage Fg.8. Results of satellte rural gray mage orgnal gray satellte reconstructed satellte mage 4.1 COMPARISON WITH OTHER EXISTING METHODS Fg.4. Results of Satellte color mage orgnal satellte urban re-constructed satellte mage Fg.5. Results of Lena gray mage orgnal lena gray reconstructed lena mage Fg.6. Results of Rose gray mage orgnal rose gray reconstructed rose mage The present Fractal Compresson [FIC] s compared wth the other exstng methods, lke standard algorthm of quadtree technque [], fractal wth quadtree and DCT technque [3], and Fractal mage compressons based on varable sze range block method [4]. The CR and PSNR values obtaned from the present method of varable range block sze for test mageres are compared wth the results of exstng methods [], [3], [4]. Standard algorthm of quadtree technque (), fractal wth quadtree and DST technque (FQandDST), FIC based on varable sze range block method (FICVRB), Proposed FIC n both color and gray level mage wth range block sze R max = 16 and R mn = 8 are comparatvely shown n the Table.3 to Table.6. Table.3. Comparson of CR wth other avalable methods for color mages Test s FQ and DST FIC Lena Satellte Rural Rose Satellte Brd The comparson chart of CR and PSNR values for the proposed method and other exstng methods n both case.e. color and grey mage when appled on test mages.e. Lena, Satellte rural mage, Satellte urban mage, Brd and Rose mages are shown n Fg.9 to Fg.1. Table.4. Comparson of CR wth other avalable methods for grey mages Test s FQ and DST FIC Lena Satellte Rural Rose
5 PSNR CR PSNR CR ISSN: (ONLINE) ICTACT JOURNAL ON IMAGE AND VIDEO PROCESSING, NOVEMBER 017, VOLUME: 08, ISSUE: 0 Satellte Brd Table.5. PSNR of the proposed method and other avalable methods of color mages FIC Test s FQ and DST FIC Lena Satellte Rose Satellte Brd Table.6. PSNR of the proposed method and other avalable methods of gray level mages Test s FQ and DST FIC Lena Satellte Rural Rose Satellte Brd Lena Satellte Rose Dataset s Satellte Brd Fg.9. Comparson chart of CR of the proposed method wth other exstng methods when appled on color test mages Lena Satellte Rose Dataset s Satellte Brd Fg.10. Exstng methods when appled on gray test mages Comparson chart of CR of the proposed method wth other Lena Satellte Rose Satellte Brd Fg.11. Comparson chart of PSNR of the proposed method wth other exstng methods when appled on color test mages Lena Database s Satellte Rose Database s Satellte FIC FIC Brd Fg.1. PSNR of the proposed method and other avalable methods of gray level mages 1643
6 NISAR AHMED AND SYED ABDUL SATTAR: FRACTAL COMPRESSION TECHNIQUE FOR COLOR IMAGES USING VARIABLE BLOCK 5. CONCLUSION In the present paper, an expermental work s done to get an mproved fractal mage compresson. The expermental results clearly depct that for the varable range block sze of R max = 16 and R mn = 8 a better result s yelded wth good mage qualty and low computatonal cost. The unqueness of the proposed method s, the RGB mage s dvded nto three planes and usng range block fractal concept t s compressed wth reduced computatonal cost. When compare wth the fxed block sze method of fractal compresson schemes, the present method exhbts hgher compresson rato and PSNR values for all types of mageres. When the proposed method s appled on both color and gray scale mages t gves approxmately same CR and PSNR values. The proposed method when appled on dfferent types of mages lke satellte mage, standard color mages and natural mage, gves comparatvely good results. The PSNR values obtaned n ths approach s always nearer to 30. REFERENCES [1] Gagnpreet Kaur, Htash Htash and Gurdev Sngh, Performance Evaluaton of Qualty based on Fractal Compresson, Internatonal Journal of Computers and Technology, Vol., No.1, pp. 0-7, 01. [] Zhuang Wu and Bx Yan, An Effectve Fractal Compresson Algorthm, Proceedngs of IEEE Internatonal Conference on Computer Applcaton and System Modelng, pp , 010. [3] Sumath Poobal and G.Ravndran, Analyss on the Effect of Tolerance Crtera n Fractal Compresson, Proceedngs of IEEE Internatonal Workshop on Imagng Systems and Technques, pp , 005. [4] A. Selm, M.M. Hadhoud, M.I. Dessouky and F.E. Abd El-Same, A Smplfed Fractal Compresson Algorthm, Proceedngs of IEEE Internatonal Conference on Computer Engneerng and Systems, pp , 008. [5] Detmar Saupe, Acceleratng Fractal Compresson by Mult-Dmensonal Nearest Neghbor Search, Proceedngs of IEEE Data Compresson, pp. -31, [6] Arnaud E. Jacqun, Codng based on a Fractal Theory of Iterated Contractve Transformatons, IEEE Transacton on Processng, Vol. 1, No. 1, pp , 199. [7] M. Barnsley, Fractals Everywhere, nd Edton, San Dego Academc Press, [8] Y. Fsher, Fractal Compresson: Theory and Applcaton, Sprnger, [9] Brendt Wohlberg and Gerhard De Jager, A Revew of the Fractal Codng Lterature, IEEE Transactons on Processng, Vol. 8, No. 1, pp , [10] Guojun Lu and Toon Ln Yew, Applcatons of Parttoned Iterated Functon Systems n and Vdeo Compresson, Journal of Vsual Communcaton and Representaton, Vol. 7, No., pp , [11] Douda Sofa, Bagr Abdallah, Abdel Hakm and Amer Elmran, A Reduced Doman Pool based on DCT for a Fast Fractal Encodng, Electronc Letters on Computer Vson and Analyss, Vol. 10, No. 1, pp. 11-3, 011 [1] Vahdat Gohar, Khodadad Habb, Yaghoob Mahd and Akbarzadeh-T Mohammad, Fractal Compresson Based on Spatal Correlaton and Hybrd Partcle Swarm Optmzaton wth Genetc Algorthm, Proceedngs of nd Internatonal Conference on Software Technology and Engneerng, pp , 010. [13] G.K. Kharate and V.H. Patl, Color Compresson Based on Wavelet Packet Best Tree, Internatonal Journal of Computer Scence Issues, Vol. 7, No., pp , 010. [14] D. Venkatasekhar and P. Aruna, A Fast Fractal Compresson usng Huffman Codng, Asan Journal of Computer Scence and Informaton Technology, Vol., No. 9, pp. 7-75, 01. [15] M. Khall, Compresson usng New Entropy Coder, Internatonal Journal of Computer Theory and Engneerng, Vol., No. 1, pp. 39-4, 010. [16] Fractal Compresson, Avalable at: [17] Mchael Barnsley and Lyman Hurd, Fractal Compresson, AK Peters Lmted, 199. [18] A.R. Nadra Banu Kamal and P. Pryanga, Iteraton Free Fractal Compresson usng Genetc Algorthm for Stll Colour s, ICTACT Journal on and Vdeo Processng, Vol. 4, No. 3, pp , 014. [19] Mohammed Ismal and S.M. Basha, Improved Fractal Compresson usng Range Block Sze, Proceedngs of IEEE Internatonal Conference on Computer Graphcs, Vson and Informaton Securty, pp , 015. [0] S.V. Veena Dev, A.G. Ananth, Fractal Compresson of Satellte res usng Varable Sze of Range Block, Proceedngs of IEEE Internatonal Conference on Sgnal and Processng Applcatons, pp , 013. [1] Maro Polvere and Napp Mchele, Speed-Up n Fractal Codng: Comparson of Methods, IEEE Transacton on Processng, Vol. 9, No. 6, pp , 000. [] A.H. Husseen, S.Sh. Mahmud and R.J. Mohammed, Compresson usng Proposed Enhanced Run Length Encodng Algorthm, Ibn AL- Hatham Journal for Pure and Appled Scence, Vol. 4, No. 1, pp. 18-5, 011. [3] K. Sharmla and K. Kuppusamy, A New Color Compresson Based on Fractal and Dscrete Cosne Transform, Internatonal Journal of Engneerng and Computer Scence, Vol. 3, No. 7, pp , 014. [4] S.V. Veenadev and A. G. Ananth, Fractal Compresson of Satellte Color res usng Varable Sze of Range Block, Internatonal Journal of Processng, Vol. 8, No. 1, pp. 1-8,
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